$\dfrac{d}{dx}[x^3]=$
$x^3$ is of the form $x^n$ and therefore we can apply the power rule: $\dfrac{d}{dx}[x^n]=n\cdot x^{n-1}$ $\begin{aligned} \dfrac{d}{dx}[x^{{3}}]&={3}x^{{3}-1} \\\\ &=3x^2 \end{aligned}$ In conclusion, $\dfrac{d}{dx}[x^3]=3x^2$